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Multilib is the idea of having side-by-side 64- and 32-bit everything on a system. To be 64-bit, a process must use exclusively 64-bit libraries. If one or more required libraries are not available in 64-bit then the application will run in 32-bit mode. These libraries are separated into two separate /lib directories: one for 64-bit, one for 32-bit.

Ideally you run most everything in 64-bit. In fact, if you know everything you'll run is 64-bit some distros (my experience is with Gentoo) allow you to disable multilib and decrease your install size.

Red Hat doesn't have an equivalent of ia32-libs. You need to install 32-bit versions of whatever software you need using yum:

yum install <package>.i586

You can use ldd to determine library dependencies, and then use yum provides to look for the appropriate package.

Lastly, make sure you're using a 64-bit JRE. I don't normally use non-Oracle JREs or JDKs so I'm not sure how the OpenJDK/IBM/etc. packages are handled, but with Oracle it's a simple matter of picking the correct version to download.